Olivia Wilde took her new fiancé, “Saturday Night Live” star Jason Sudeikis, on a raunchy date to a New York strip club, booking a private room with two pole dancers before picking up the tab, sources tell Page Six.

In a move that could turn already alluring Wilde into the most desirable fiancée on Earth, the actress took Sudeikis for a fun night out at the Penthouse Executive Club on West 45th Street.

There, a witness told us, “Olivia booked the private champagne room with two dancers. She took Jason inside, and while he wasn’t allowed to touch the dancers, she could touch them.”

The source continued with a lot more detail that cannot be printed in a family newspaper or gossip column, adding, “They were in there for two hours, Olivia picked up the entire tab. Jason is a lucky guy.”

We’re told the wild date took place just over a month ago, after Wilde and Sudekis announced their engagement in January.

The actress has had some experience in the exotic-dancing department. She played a stripper in the 2012 comedy “Butter,” in which her character performs a lap dance for Ty Burrell and also smooches with Ashley Greene.

She joked at a press conference for the film that she would advise fellow actors: “Take risks, and take your clothes off — even if they don’t ask. Leave your comfort zone.”

Of preparing for the role, she told Page Six, “We went down to Action Central Cabaret in Shreveport, La., and I got to hang out in the locker room with the strippers, and they were so sweet . . . I learned that what they do is incredibly difficult . . . It’s really an under-appreciated dance form.” Wilde also read Diablo Cody’s book “Candy Girl,” about Cody’s year as a stripper.

Wilde, who also strips off in the new movie “Drinking Buddies,” has previously described how she was “blissfully, hopefully, wildly in love” with Sudeikis, adding they “have sex like Kenyan marathon runners.”

Sudeikis’ rep commented, “Are you saying the New York Post is a family newspaper?”